Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of 20 school cricketers age (A=12, N=20)

⇒S=12 X 20 =240

Later, Age of the coach included, the average becomes 15 yr (so A=15, N=21)

So, sum of 20 cricketers and a coach age

⇒S=15 X 21 =315

Now,

The age of the coach =(sum of 20 school cricketers age)-(Sum of 20 cricketers and a coach age)

=315-240

=75

Hence, Option D is correct.